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Results tagged with lo.logic
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user 65
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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Logical problems in category theory
Every question asked can be divided into two parts: what is known, and what is asked.
I think your question's "what is known" part is by no means universally agreed. It's not frustrating to hear peop …
- 15.1k
4
votes
How many of the true sentences are provable?
Update: in response to comment below, I'm not sure anymore the probability in question was 0.
Let's try the measure that gives an equal weight for any true statement of fixed length $N$ (written in m …
- 15.1k
0
votes
Why do I find Category Theory mostly just a way to make simple things difficult?
I think for mathematicians, especially the algebraic geometers, category theory has a somewhat different meaning that in your area.
For us, it's primarily an important and quite straightforward way t …
- 15.1k
3
votes
Can we disallow finite choice?
Yes, this framework is called category theory.
Let's indeed start with the example of vector spaces. What you do is you say that some operations are natural. These operations should make sense not on …
- 15.1k
27
votes
6
answers
9k
views
What is a topos?
According to Higher Topos Theory math/0608040 a topos is
a category C which behaves like the
category of sets, or (more generally)
the category of sheaves of sets on a
topological space.
Could one …
- 15.1k
2
votes
Several Topos theory questions
(1) Yes, I think that's one of the ways to define schemes. Look for representable functors and you'll get lots of literature.
It was a crazy idea about 50 years go, part of establishment nowadays.
…
- 15.1k
7
votes
1
answer
2k
views
Polynomial representing prime numbers
Along the lines of Polynomial representing all nonnegative integers, but likely well-known question:
is there a polynomial $f \in \mathbb Q[x_1, \dots, x_n]$ such that $f(\mathbb Z\times\mathbb Z\ …
- 15.1k